This question intrigued me a lot since if animals in the wild did have menstruation with blood flow, wouldn't all that blood be attracting every other predator in the vicinity?
I would guess that the answer is something like this: ever since the development of the placenta enabled females to carry their offspring longer and to develop more fully. Upon birth they were stronger and/or their brains were more fully developed (in the case of humans). The increased gestation time, made possible by the structures of the womb and placenta is probably an adaptation whose advantages are much greater than the increased risk from menstruation once a month.
Some anthropological studies indicate that in preindustrial societies that women do not menstruate very much as adults though. If you subtract out the time that they are carrying infants and nursing, which both prevent menstrual cycles, females will miss years of menstruation with only a few months in between. I would assume this is a factor in the risk of menstruation for many animals.